Find the partial fraction decomposition of

Answer:

if this is geometry nation, the answer is c, 4671 sq cm

Step-by-step explanation:

Final answer:

The surface area of the triangular prism container needed to enclose the rolled document with a diameter of 10 cm and a length of 85 cm is 1695 cm².

Explanation:

To find the surface area of a triangular prism container, we need to consider the three rectangular faces and two triangular faces of the prism. The rectangular faces have the same dimensions as the rolled document, which is 10 cm in diameter and 85 cm in length. So, the area of each rectangular face is 10 cm x 85 cm = 850 cm².

For the triangular faces, we need to calculate the base and height. The base of the triangle is the same as the diameter of the rolled document, which is 10 cm. The height of the triangle can be found using the Pythagorean theorem, where the hypotenuse is the length of the rolled document (85 cm) and the base is half the diameter (5 cm). The height is then calculated as √(85 cm)² - (5 cm)² = 84.5 cm.

The area of each triangular face is 1/2 x base x height = 1/2 x 10 cm x 84.5 cm = 422.5 cm². Since there are two triangular faces, the total area of the triangular faces is 2 x 422.5 cm² = 845 cm².

Finally, to find the surface area of the triangular prism container, we add the areas of the rectangular faces and triangular faces: 850 cm² + 845 cm² = 1695 cm².

It depends on how many different options there are on the spinner

9 different sums are possible from the given data

To calculate the number of different sums possible, let's break down the problem step by step:

1. Determine the number of cards in each set:

  - Set 1: 1, 2, 3, 4, 5 (5 cards)

  - Set 2: 6, 7, 8, 9, 10 (5 cards)

2. Find the total number of combinations by multiplying the number of cards in each set:

  - Total combinations = 5 (cards in Set 1) × 5 (cards in Set 2) = 25 combinations

Now, let's consider all the possible sums:

- The lowest possible sum is when we pick the lowest card from each set: 1 + 6 = 7.

- The highest possible sum is when we pick the highest card from each set: 5 + 10 = 15.

To find all the possible sums, we consider the range from the lowest sum to the highest sum, inclusive:

7, 8, 9, 10, 11, 12, 13, 14, 15

There are 9 different sums in total.

So, the correct answer is: 9 different sums are possible.

The key to solving this problem lies in understanding the concept of combinations and the range of possible sums. We find the number of combinations by multiplying the number of cards in each set. Then, by considering the lowest and highest cards from each set, we determine the range of possible sums. Finally, by listing out all the sums within that range, we find that there are 9 different sums possible. This method ensures a systematic approach to solving the problem, providing a clear and accurate answer.

Complete question:

You pick one card from each set, spin the spinner, and find the sum. How many different sums are possible

Answer:

0.04746

Step-by-step explanation:

To answer this one needs to find the area under the standard normal curve to the left of 5 minutes when the mean is 4 minutes and the std. dev. is 0.6 minutes.  Either use a table of z-scores or a calculator with probability distribution functions.

In this case I will use my old Texas Instruments TI-83 calculator.  I select the normalcdf( function and type in the following arguments:  :

normalcdf(-100, 5, 4, 0.6).  The result is 0.952.  This is the area under the curve to the left of x = 5.  But we are interested in finding the probability that a conversation lasts longer than 5 minutes.  To find this, subtract 0.952 from 1.000:   0.048.  This is the area under the curve to the RIGHT of x = 5.

This 0.048 is closest to the first answer choice:  0.04746.

Answer:

20.7 years

Step-by-step explanation:

Use the "compound amount, compounding continuously" formula:

A = Pe^(r · t)  

Here,

A = $2,500 = $1,450e^(0.06 · t)

Divide both sides by $1,450:  1.724 = e^(0.06 · t)

Taking the natural log of both sides, we obtain:

ln 1.724 = (0.06 · t).

Finally, we divide both sides by 0.06, obtaining:

ln 1.724

------------ = t = 20.7

   0.06

The Investment will reach a value of $2.500 in approximately 20.7 years.

Answer:

Years = natural log (total / principal) / rate

Years = natural log (2,500 / 1,450) / .06

Years = natural log (1.724137931) / .06

Years = 0.54472717542 / .06

Years = 9.078786257

Years = 9.1 (rounded)

Step-by-step explanation:

Answer:

y = |x| + 7

Step-by-step explanation:

Use desmos.com to see it in action

The answer is Y=|x| +7

Answer:

x = 10.1

Step-by-step explanation:

The function SINE stands for Opp. / Hyp. the function that should be used is COSINE. We now know that cos(39) = x/13 and using a calculator we can substitute for cos(39).

Make sure your calculator is in degrees when plugging into your calculator so you don't use radians.

We get 0.777145961457 = x/13 now since we have substituted we can multiply both sides of the equation to get 10.1028974989 = x. When rounded, it is 10.1 units.

Answer:

= 14

Step-by-step explanation:

Given a right angled triangle with hypotenuse length c =18.6 and ∠B = 43°.

We can use the trigonometric forms of a right angled triangle,

That is;

Cos 43 = Adjacent/Hypotenuse

That is;

Cos 43 = BC/AC = a/c

Therefore;

Cos 43 = a/18.6

a = 18.6 × cos 43

   = 13.603

   = 14

Therefore, BC or a is 14 (to the nearest whole number)

In the triangle:

Y= 4.4 centimeters

Answer:

  216 m³

Step-by-step explanation:

The ratio of linear dimensions is the square root of the ratio of area dimensions.

  s = √(216/1014) = √(36/169) = 6/13

Then the ratio of volume dimensions is the cube of that. The smaller volume is ...

  v = (6/13)³·2197 m³ = 216/2197·2197 m³ = 216 m³

The volume of the smaller solid is 216 m³.

Answer:

h=1    K =2    a =6    b=2

Step-by-step explanation:

look this solution :

Answer:

h = 1, k = 2, a = 6 and b = 2.

Step-by-step explanation:

Start by grouping the terms in x and y together:

4x^2 - 8x  + 36y^2 - 144y = -4

Factor out the coefficient:

4(x^2 - 2x) + 36(y^2 - 4y) = -4

Complete the squares:

4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4

4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4

4(x - 1)^2 + 36(y - 2)^2 =  144

Divide through by 144:

(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1

(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1  (answer).

Answer:

It is the second choice.

Step-by-step explanation:

-1/2 x ≥ 4

x ≤ 4 * -2

x  ≤  -8.

The number line with  solid circle at -8 and shaded region extending to the left, serves as the appropriate number line representation for the inequality -1/2x ≥ 4. It clearly conveys that all values of x less than or equal to -8 are part of the solution set.

The correct answer is option B.

To represent the solution set of an inequality, we employ a number line with various markings to indicate the values that satisfy the inequality's criteria. In this case, we're dealing with the inequality -1/2x ≥ 4.

The inequality symbol ≥ signifies that the value on the left-hand side is greater than or equal to the value on the right-hand side. When we rewrite the inequality as x ≤ -8, we're essentially saying that any value of x less than or equal to -8 satisfies the inequality.

Option B accurately represents this solution set through a solid circle at -8, indicating that -8 is a direct solution to the inequality. The shaded region extending to the left of -8 further emphasizes that all values of x less than -8 also satisfy the inequality.

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Answer:

A) If the domain of y=cos(x) is restricted to [0, π], y=cos^-1(x) is a function.

Step-by-step explanation:

In order for the inverse function to be a function, the original must pass the horizontal line test: a horizontal line must intersect the function in only one place.

As you can see from the attached graph, restricting the cosine function to the domain [0, π] allows it to pass the horizontal line test, so its inverse will be a function.

__

Restricting the domain to [-π/2, π/2] does not limit cos(x) to something that will pass the horizontal line test.

Answer:

[tex]\large\boxed{\sum\limits_{k=3}^5(-2k+5)=-9}[/tex]

Step-by-step explanation:

[tex]\sum\limits_{k=3}^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_{k=3}^5(-2k+5)=-1+(-3)+(-5)=-9[/tex]

Answer with explanation:

Coordinates of A, B, C, and D are  (-8, 1), (-2, 4), (-3, -1), and (-6, 5).

Plotting the points on two dimensional plane

1. You will find that, the four points, A , B , C and D do not lie on the dame Line.

[tex]\text{Slope of AB}=\frac{4-1}{-2+8}=\frac{3}{6}=\frac{1}{2}\\\\\text{Slope of CB}=\frac{4+1}{-2+3}=\frac{5}{1}=5\\\\\text{Slope of CD}=\frac{5+1}{-6+3}=\frac{6}{-3}=-2\\\\\text{Slope of AD}=\frac{5-1}{-6+8}=\frac{4}{2}=2\\\\\text{Slope of BD}=\frac{5-4}{-6+2}=\frac{1}{-4}=\frac{-1}{4}\\\\\text{Slope of AC}=\frac{-1-1}{-3+8}=\frac{-2}{5}[/tex]

→→None of the two lines are Parallel nor they are perpendicular,because neither product of slopes of two lines is equal to ,-1, nor the slope of two lines are equal.

It means they are Intersecting Lines .

Option D:⇒ And are intersecting lines but are not perpendicular.

Answer:

line AB and line CD are perpendicular lines

Step-by-step explanation:

Answer:

16w^4

Step-by-step explanation:

(2w)^4 is just 2w mulitplied by itself 4 times. we can do this step by step and multiply the 2 by itself 4 times first:

2 x 2 x 2 x 2 or 2^4 = 16

next we can multiply w by itself 4 times:

w x w x w x w or w^4 = w^4

our answer would be 16w^4

you can also multiply it without breaking it down like this:

2w x 2w x 2w x 2w = 16w^4

The simplification of an expression [tex](2w)^{4}[/tex] without parentheses is [tex]16w^{4}[/tex].

Given:

Find:

Solution:

The given expression is [tex](2w)^{4}[/tex].

This means that 2w has to be multiplied itself by 4.

So, 2*2*2*2 = 16

and w*w*w*w = [tex]w^{4}[/tex]

So, the expression [tex](2w)^{4}[/tex] = [tex]16w^{4}[/tex]

Therefore, The simplification of the expression [tex](2w)^{4}[/tex] is [tex]16w^{4}[/tex]

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The answer is D, he has to hit 1/6 sides so the chances are 5/6 hit hits 1,3,4,5, or 6

Answer:

D

Step-by-step explanation:

there are six sides on a die and only one side with a 2 so you have 1 side witha two 6-1=5 =5/6

Make because it’s statistical and his question is more specific

In the given question, Mark is correct.

A statistical question is one that can be answered by collecting data from several sources.

The question Elsie asked is a yes/no question, you can't answer the question in terms of data/numbers, but the question mark asked has to be answered in terms of data/numbers, hence it is a statistical question.

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Answer:

a) 180

b) CJ= 5.83095189485

CK= 9.89949493661

CL= 8.0622577483

c) All angles formed by a point and its image, with the vertex at the center of rotation, are congruent. Each point on the original figure is the same distance from the center of rotation as its image.

Step-by-step explanation:

Answer:

5 5/7 units

Step-by-step explanation:

Length = x

Width = 3/4 x

Perimeter = 20 units

2( x + 3/4 x) = 20

x + 3/4 x = 10

7/4 x = 10

x = 40/7 = 5 5/7 units

The width of the rectangle with a perimeter of 20 units and a width that is 3/4 of its length is 6 units.

The student's question relates to the perimeter of a rectangle that's been given as 20 units and the width as 3/4 of the length. To find the width, we first need to set up an equation based on the formulas for a rectangle's perimeter and the information provided.

The perimeter of a rectangle is given by the formula 2(length + width), or more simply 2L + 2W. Because the question states that the width (W) is 3/4 times the length (L), or W = 0.75L, this can be substituted into our initial formula. Our formula therefore becomes 2L + 2(0.75L) = 20, which simplifies to 2.5L = 20. If you divide both sides of this equation by 2.5, you find L = 8.

Having found the length, you can now find the width by using the relationship given in the question: W = 0.75L. Substituting 8 for L, we find W = 6 units.

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Answer:

18 in^2.

Step-by-step explanation:

The ratio of their areas = the ratio of the squares of corresponding sides. So:

9^2 / 12^2 = x / 32

81/144 = x / 32

x =  (81 * 32) / 144

=  18 in^2.

You must know that % is a number out of 100.

Therefore given 91/100 trusted DNA surveying, we know as a percentage this is 91% from the equation below:

(91/100)*100=91

We can conclude that 1%=1 person.

Although the difference is only 1 (91-90=1), the actual proportion of people who trust DNA testing is larger than the 90% by 1%.

Testing the hypothesis, it is found that since the p-value of the test is of 0.37 > 0.01, there is not enough evidence to conclude that the actual proportion of people who trust DNA testing larger than 90%.

At the null hypothesis, we test if the proportion is of 90%, that is:

[tex]H_0: p = 0.9[/tex]

At the alternative hypothesis, it is tested if the proportion is larger than 90%, that is:

[tex]H_1: p > 0.9[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are: [tex]n = 100, \overline{p} = \frac{91}{100} = 0.91, p = 0.9[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.91 - 0.9}{\sqrt{\frac{0.9(0.1)}{100}}}[/tex]

[tex]z = 0.33[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.91, which is 1 subtracted by the p-value of z = 0.33.

Looking at the z-table, z = 0.33 has a p-value of 0.63.

1 - 0.63 = 0.37.

Since the p-value of the test is of 0.37 > 0.01, there is not enough evidence to conclude that the actual proportion of people who trust DNA testing larger than 90%.

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The answer is (-4x-1)(2x^2+3) when factoring this expression by grouping

Answer:

The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]-8x^3-2x^2-12x-3[/tex]

The above expression can be written as:

[tex](-8x^3-2x^2)+(-12x-3)[/tex]

Take out the greatest common factor from each group.

[tex]-2x^2(4x+1)-3(4x+1)[/tex]

Further solve the above expression.

[tex](4x+1)(-2x^2-3)[/tex]

Hence, the required expression is

[tex](4x+1)(-2x^2-3)[/tex]

The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]

Check the picture below.

The answer is C. (5,3)

Explanation:

(X,Y) is how ordered pairs should be set up.

Answer:

C (5,3)

Step-by-step explanation:

The first point in an ordered pair is the x coordinate.

We move 5 units to the right, so it is +5

The second coordinate is the y coordinate.

We move 3 units up, so it is +3

(5,3)

11.99 + d= 14.98

To get this answer you must come up with a simple equation at first. The total cost of the meal is $14.48 and without the drink it is $11.98.To calculate the drink price you must perform the equation, 14.48-11.98=d. Yet, that is still not in the array of choices. So, you have to add 11.98 on both sides. This will cancel out the 11.98 on the left side and give you 14.48=11.98+d and using the reflexive property you will get 11.98+d=14.48.

11.98+d=14.4 this equation can be used to find the cost of the drink.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. Assuming that an is a number, a = a.

Given

The total cost of the meal is $14.48 and without the drink it is $11.98.To calculate the drink price you must perform the equation, 14.48-11.98=d. Yet, that is still not in the array of choices. So, you have to add 11.98 on both sides. This will cancel out the 11.98 on the left side and give you 14.48=11.98+d and using the reflexive property you will get 11.98+d=14.48.

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Answer:

Angle B is 45°

Step-by-step explanation:

Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.

The Angle B is 45°

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Given

Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.

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Answer:

75 miles

Step-by-step explanation:

Let x mph be the cyclist A rate, then x+3 mph is the cyclist B rate.

1. In 1 hour they both traveled x+x+3=2x+3 miles. In 5 hours they traveled

[tex]5(2x+3)=10x+15\ miles.[/tex]

2. Cyclist A spent [tex]\frac{31.8}{x}[/tex] hours to travel 31.8 miles. If the cyclist from B had started moving 30 minutes (1/2 hour) later than the cyclist A, then he spent [tex]\frac{31.8}{x}-\frac{1}{2}[/tex] hours to travel the rest of the distance. In total they both traveled the whole distance 10x+15 miles, thus

[tex]31.8+\left(\dfrac{31.8}{x}-\dfrac{1}{2}\right)\cdot (x+3)=10x+15[/tex]

Solve this equation. Multiply it by 2x:

[tex]63.6x+(63.6-x)(x+3)=2x(10x+15)\\ \\63.6x+63.6x+190.8-x^2-3x=20x^2+30x\\ \\-x^2+124.2x+190.8-20x^2-30x=0\\ \\-21x^2+94.2x+190.8=0\\ \\210x^2-942x-1908=0\\ \\35x^2-157x-318=0\\ \\D=(-157)^2-4\cdot 35\cdot (-318)=69169\\ \\x_{1,2}=\dfrac{-(-157)\pm\sqrt{69169}}{2\cdot 35}=\dfrac{157\pm263}{70}=-\dfrac{106}{70},\ 6[/tex]

The rate cannot be negative, thus, x=6 mph.

Hence, the distance between cities A and B is

[tex]10\cdot 6+15=60+15=75\ miles.[/tex]

[tex]g\circ f(-9)=g(f(-9))[/tex]

By definition of [tex]f[/tex],

[tex]f(-9)=3\cdot9-8=19[/tex]

and by definition of [tex]g[/tex],

[tex]g\circ f(-9)=g(f(-9))=g(19)=\sqrt{14-19}-10=\sqrt{-5}-10[/tex]

which is undefined if [tex]f,g[/tex] are supposed to be real-valued functions. If they're complex-valued, then [tex]\sqrt{-5}=i\sqrt 5[/tex] and [tex]g\circ f(-9)=-10+i\sqrt 5[/tex].

Answer:

The margin of error is approximately 0.3

Step-by-step explanation:

The following information has been provided;

The sample size, n =225 students

The sample mean number of hours spent studying per week = 20.6

The standard deviation = 2.7

The question requires us to determine the margin of error that would be associated with a 90% confidence level. In constructing confidence intervals of the population mean, the margin of error is defined as;

The product of the associated z-score and the standard error of the sample mean. The standard error of the sample mean is calculated as;

[tex]\frac{sigma}{\sqrt{n} }[/tex]

where sigma is the standard deviation and n the sample size. The z-score associated with a 90% confidence level, from the given table, is 1.645.

The margin of error is thus;

[tex]1.645*\frac{2.7}{\sqrt{225}}=0.2961[/tex]

Therefore, the margin of error is approximately 0.3

Answer:

.3 is the answer.

Step-by-step explanation:

Answer:

Option B

Part a) The focus is [tex](1/28,0)[/tex]

Part b) The directrix is [tex]x=-1/28[/tex]

Part c) The equation is  [tex]y^{2}= (1/7)x[/tex]

Step-by-step explanation:

step 1

Find the equation of the parabola

we know that

The parabola in the graph has a horizontal axis.

The standard form of the equation of the horizontal parabola is

[tex](y - k)^{2}= 4p(x - h)[/tex]

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h + p, k).

The directrix is the line x= h- p.

The axis is the line y = k.

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left

In this problem we have that the vertex is the origin

so

(h,k)=(0,0)

substitute in the equation

[tex](y - 0)^{2}= 4p(x - 0)[/tex]

[tex]y^{2}= 4p(x)[/tex]

The points (7,1) and (7,-1) lies on the parabola-----> see the graph

substitute the value of x and the value of y in the equation and solve for p

[tex](1)^{2}= 4p(7)[/tex]

[tex]1= 28p[/tex]

[tex]p=1/28[/tex]

The equation of the horizontal parabola is

[tex]y^{2}= 4(1/28)(x)[/tex]

[tex]y^{2}= (1/7)x[/tex]

step 2

Find the focus

we know that

The focus is at (h + p, k)

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex](0+1/28,0)[/tex]

therefore

The focus is at

[tex]F (1/28,0)[/tex]

step 3

Find the directrix

The directrix is the line x = h- p

Remember that

[tex](h,k)=(0,0)[/tex]

[tex]p=1/28[/tex]

substitute

[tex]x=0-1/28[/tex]

[tex]x=-1/28[/tex]

Answer:

B

Step-by-step explanation:

Confirmed on E D G 2021